Presence of interaction between a genotype and certain factor in determination of a trait's value, it is expected that the trait's variance is increased in the group of subjects having this genotype. Thus, test of heterogeneity of variances can be used as a test to screen for potentially interacting single-nucleotide polymorphisms (SNPs). In this work, we evaluated statistical properties of variance heterogeneity analysis in respect to the detection of potentially interacting SNPs in a case when an interaction variable is unknown.
Through simulations, we investigated type I error for Bartlett's test, Bartlett's test with prior rank transformation of a trait to normality, and Levene's test for different genetic models. Additionally, we derived an analytical expression for power estimation. We showed that Bartlett's test has acceptable type I error in the case of trait following a normal distribution, whereas Levene's test kept nominal Type I error under all scenarios investigated. For the power of variance homogeneity test, we showed (as opposed to the power of direct test which uses information about known interacting factor) that, given the same interaction effect, the power can vary widely depending on the non-estimable direct effect of the unobserved interacting variable. Thus, for a given interaction effect, only very wide limits of power of the variance homogeneity test can be estimated. Also we applied Levene's approach to test genome-wide homogeneity of variances of the C-reactive protein in the Rotterdam Study population (n = 5959). In this analysis, we replicate previous results of Pare and colleagues (2010) for the SNP rs12753193 (n = 21, 799).
Screening for differences in variances among genotypes of a SNP is a promising approach as a number of biologically interesting models may lead to the heterogeneity of variances. However, it should be kept in mind that the absence of variance heterogeneity for a SNP can not be interpreted as the absence of involvement of the SNP in the interaction network.